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# If a, b, and c are nonzero numbers and a + b = c, which of t

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Math Expert
Joined: 02 Sep 2009
Posts: 51045
If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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17 Feb 2014, 02:45
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Question Stats:

90% (01:05) correct 10% (01:12) wrong based on 462 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1 ?

(A) (a - b)/c
(B) (a - c)/b
(C) (b - c)/a
(D) (b - a)/c
(E) (c - b)/a

Problem Solving
Question: 99
Category: Arithmetic Operations on rational numbers
Page: 74
Difficulty: 550

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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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17 Feb 2014, 10:27
5
a + b = c ,
taking b to the other side, a = c-b ,
take a to the other side , 1 =$$\frac{c-b}{a}$$

option E.
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Math Expert
Joined: 02 Sep 2009
Posts: 51045
Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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17 Feb 2014, 02:45
SOLUTION

If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1 ?

(A) (a - b)/c
(B) (a - c)/b
(C) (b - c)/a
(D) (b - a)/c
(E) (c - b)/a

From a + b = c:

a = c - b;
b = c - a;
c = a + b.

Only option E yields 1: (c - b)/a = a/a = 1.

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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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17 Feb 2014, 04:47
1
Since we are given that a+b=c, the answer we have to pick has to be in one of the following forms:

a= c-b
b= c-a
c= a+b

The only valid choice is (E), since it is dividing equal values.
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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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17 Feb 2014, 08:18
1
Option E.
(c-b)/a=(a+b-b)/a=1
Given c=a+b

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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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18 Feb 2014, 06:45
2
I know it is not the quickest/best approach but I used number picking strategy: a=3; b=4; c=7;

Sub these values and you can clearly find out that answer is 1, especially if you are not so good at using variables.
Math Expert
Joined: 02 Sep 2009
Posts: 51045
Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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22 Feb 2014, 04:48
SOLUTION

If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1 ?

(A) (a - b)/c
(B) (a - c)/b
(C) (b - c)/a
(D) (b - a)/c
(E) (c - b)/a

From a + b = c:

a = c - b;
b = c - a;
c = a + b.

Only option E yields 1: (c - b)/a = a/a = 1.

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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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20 Mar 2014, 23:38
2
One more method

Looking at the equation a+b = c,

we can conclude that c > a & c > b

Option A & Option D are not possible as a & b are on the same side of equation.

Option B & Option C will be negative as c > a & c > b

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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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01 Apr 2015, 11:19
Another way would be to just plug-in numbers for a,b and c.
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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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02 Apr 2015, 21:38
Hi All,

This question is perfect for TESTing VALUES.

We're told that A, B and C are non-zero numbers and that A + B = C. We're asked which of the following answers is equal to 1.

IF....
A = 2
B = 3
C = 5

Answer A: (2-3)/5 = -1/5 NOT a match
Answer B: (2-5)/3 = -3/3 NOT a match
Answer C: (3-5)/2 = -2/2 NOT a match
Answer D: (3-2)/5 = 1/5 NOT a match
Answer E: (5-3)/2 = 2/2 This IS a match

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If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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22 Aug 2015, 23:24
We know that a + b = c.
So, c > b > a

Any option which has a - b, b - c, or a - c as numerator options will be incorrect --> such an option will deduce negative value.
This rules out option A, B and C.

It is also noteworthy that c cannot be in the denominator as it is the biggest of the three and the solution will be < 1.
This rules out option D.

Only option left is option E. You can either mark it, it test the option.

Another way would be to just solve the parent equation -
a + b = c
a = c - b
1 = (c - b)/a --> Answer choice E!

Cheers!
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Re: If a, b, and c are nonzero numbers and a + b = c, which of t  [#permalink]

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05 Mar 2018, 08:38
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a, b, and c are nonzero numbers and a + b = c, which of the following is equal to 1 ?

(A) (a - b)/c
(B) (a - c)/b
(C) (b - c)/a
(D) (b - a)/c
(E) (c - b)/a

Problem Solving
Question: 99
Category: Arithmetic Operations on rational numbers
Page: 74
Difficulty: 550

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

let a, b, c be 1, 2, 3 respectively.

test the values.

only E yields 1
Re: If a, b, and c are nonzero numbers and a + b = c, which of t &nbs [#permalink] 05 Mar 2018, 08:38
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